Machines of this type are known, for example, from EP 1 288 129. This document describes a shrink-fit tunnel in which packaged goods, such as packing units with bottles, cans or the like are conveyed on a conveyor belt through a tunnel. In the tunnel, hot air blowers ensure that the shrink film surrounding the packaged goods is heated and shrunk onto the packing unit. However, these known shrink-fit tunnels have the disadvantage that, due to the conveying movement of the packing unit in the tunnel and the design of the tunnel for packaged goods of different sizes, said tunnels are relatively long and relatively high. Consequently, the tunnel volume is relatively large. Therefore, since the entire tunnel has to be heated and has relatively large entry and exit openings, a large part of the energy produced by the hot air blowers is lost.